The puritans did have some variety when it came to views or practices regarding fast and thanksgiving days (such as recurrence, and the Scots were uncomfortable with the in perpetuity monthly fast in England called for until the war was over). Gillespie acknowledges the call for providential fasts or thanksgiving days.
2. God has given His church a general precept for extraordinary fasts (Joel 1:14; 2:15), as likewise for extraordinary festivities to praise God, and to give Him thanks in the public assembly of His people, upon the occasional motive of some great benefit which by the means of our fasting and praying we have obtained (Zech. 8:19 with Zech. 7:3).
In the case of Purim as far as what happened at the time, he's of one school of thought as far as only civil joy, etc. I tend of agree with Thomas M'Crie the elder who disagrees with Gillespie and that school. Gillespie's English Popish Ceremonies is a remarkable work, for a 22-23 year old, but isn't a perfect work (there are actual mistakes).
That being said, M'Crie takes the same view in end as far as recurrence and as far as the attempt to color out of the lines and argue from occasional days of fasting and thanksgiving to the set apart "holy" days as actually holy, like the Lord's Day, against which is what Gillespie et al were arguing. Here M'Crie, it is not that long. The text below comes from
The Religious Observance of Christmas and ‘Holy Days’ in American Presbyterianism.
Appendix 1: Thomas M’Crie on The Days of Purim
[In the following extract Dr. M’Crie addresses the nature of the days of Purim, the authority of their appointment, and the relevance of these days to ‘holy days’ and the Westminster Confession’s days of fasting and thanksgiving. ]
The feast referred to in our text is called the feast of Purim, or Lots, from the Persic word pur, which signifies the lot; and the name was given it because Haman had cast lots to determine the day on which he should destroy all the Jews; but He who has the disposal of the lot, “caused his wicked device to return on his own head,” and saved his people.
There are two questions respecting this feast. What was its nature? And by what authority was it enjoined?
What was its nature? Was it religious, or merely civil? Some interpreters are of opinion that it was entirely civil or political, and intended to commemorate a temporal deliverance, by such expressions of outward joy as are common among all people on such occasions. In corroboration of this opinion, they observe that nothing peculiarly sacred is mentioned as belonging to its celebration, but only eating and drinking, rejoicing, and sending portions to one another, and gifts to the poor; that they were not restricted from ordinary work, but merely rested from the trouble and sorrow which they had lately felt. But though it should be granted that the description contains nothing but expressions of secular joy, we would scarcely be warranted to maintain that this feast had no religious character. It is of the nature of this Book not to bring forward religion expressly, for reasons that we formerly assigned. Would we say that the fast formerly observed by Esther and the Jews in Shushan consisted solely in abstinence from food, because there is no mention of prayer combined with it? Nay, we find this exercise specified in the account of the feast: “they had decreed for themselves and for their seed the matters of their fastings and their cry,” that is, their prayer (v.31). Now, though this should be understood as looking back on their exercise when the murderous edict was first promulgated, yet its being named here gives a religious character to the feast. Can we suppose that they would fast and pray during their distress, and not rejoice before the Lord, and give thanks to him after he had hearkened to them? But it is more natural to understand the words prospectively, and they may be translated thus – “adding fasting and prayer.” Accordingly, in after times, the Jews kept the thirteenth of Adar as a fast, and the two following days as a feast.
By what authority was it enjoined? Or, in other words, did the observance of it rest on mere human authority? Did Mordecai, in proposing it, act from the private motion of his own mind; and, in confirming it, did he proceed entirely upon the consent of the people? Or was he guided in both by divine and extraordinary counsel, imparted to him immediately, or by some prophetic person living at that time? That the vision and the prophecy were still enjoyed by the Jews dwelling in Persia, cannot be denied by those who believe the canonical authority of this book, and what is contained in that of Ezra. We have already seen reasons for thinking Mordecai acted under the influence of the faith of Moses’ parents, from the time that he proposed his cousin Esther as a candidate to succeed Vashti the queen. There can be no doubt that he was raised up in an extraordinary manner as a saviour to Israel; and in the course of this Lecture we have seen grounds for believing that, in addition to his other honours, he was employed as the penman of this portion of inspired scripture. From all these considerations, it is reasonable to conclude that the feast of Purim was not instituted without divine counsel and approbation. Add to this, that the decree of Esther confirming it, is expressly said, in the close of this chapter, to have been engrossed in this book, by whomsoever it was written.
From what has been said, we may infer that this passage of Scripture gives no countenance to religious festivals, or holidays of human appointment, especially under the New Testament. Feasts appear to have been connected with sacrifices from the most ancient times; but the observance of them was not brought under any fixed rules until the establishment of the Mosaic law. Religious festivals formed a noted and splendid part of the ritual of that law; but they were only designed to be temporary; and having served their end in commemorating certain great events connected with the Jewish commonwealth, and in typifying certain mysteries now clearly revealed by the gospel, they ceased, and, along with other figures, vanished away. To retain these, or to return to them after the promulgation of the Christian law, or to imitate them by instituting festivals of a similar kind, is to doat on shadows — to choose weak and beggarly elements — to bring ourselves under a yoke of bondage which the Jews were unable to bear, and interpretatively to fall from grace and the truth of the gospel. “Ye observe days and months, and times and years. I am afraid of you, lest I have bestowed upon you labour in vain.” “Let no man therefore judge you in meat, or in drink, or in respect of an holiday, or of the new moon, or of the Sabbath days, which are a shadow of things to come.” Shall we suppose that Christ and his apostles, in abrogating those days which God himself had appointed to be observed, without instituting others in their room, intended that either churches or individuals should be allowed to substitute whatever they pleased in their room? Yet the Christian church soon degenerated so far as to bring herself under a severer bondage than that from which Christ had redeemed her, and instituted a greater number of festivals than were observed under the Mosaic law, or even among pagans.
To seek a warrant for days of religious commemoration under the gospel from the Jewish festivals, is not only to overlook the distinction between the old and new dispensations, but to forget that the Jews were never allowed to institute such memorials for themselves, but simply to keep those which infinite Wisdom had expressly and by name set apart and sanctified. The prohibitory sanction is equally strict under both Testaments: “What thing soever I command you, observe to do it: thou shalt not add thereto, nor diminish from it.”
There are times when God calls, on the one hand, to religious fasting, or, on the other, to thanksgiving and religious joy; and it is our duty to comply with these calls, and to set apart time for the respective exercises. But this is quite a different thing from recurrent or anniversary holidays. In the former case the day is chosen for the duty, in the latter the duty is performed for the day; in the former case there is no holiness on the day but what arises from the service which is performed on it, and when the same day afterwards recurs, it is as common as any other day; in the latter case the day is set apart on all following times, and may not be employed for common or secular purposes. Stated and recurring festivals countenance the false principle, that some days have a peculiar sanctity, either inherent or impressed by the works which occurred on them; they proceed on an undue assumption of human authority; interfere with the free use of that time which the Creator hath granted to man; detract from the honour due to the day of sacred rest which he hath appointed; lead to impositions over conscience; have been the fruitful source of superstition and idolatry; and have been productive of the worst effects upon morals, in every age, and among every people, barbarous and civilized, pagan and Christian, popish and protestant, among whom they have been observed. On these grounds they were rejected from the beginning, among other corruptions of antichrist, by the reformed Church of Scotland, which allowed no stated religious days but the Christian Sabbath.